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 Topic: sequences
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A pattern rule for a sequence 2016-10-28
From Grace:
Here's a Grade 7 question, we need to find the pattern rule:

1 - 1
2 - 3
3 - 6
4 - 10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace.

Two sequences 2016-08-20
From Ting:
The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please)
Some non-decreasing sequences 2015-04-13
From Sky:
Hi I'm a Student and i'll try my best to state the problem perfectly.

The number of non-decreasing sequences of size at least 1 and at most N, such that each element of the sequence lies between L and R, both inclusive.

Eg:- N=1 L=4 R=5
ans= 2. [{4},{5}]

N=3 L=4 R=6
ans= 19. [{4},{5},{6},{4,4},{4,5},{4,6},{5,5},{5,6},{6,6} {4,4,4},{4,4,5},{4,4,6},{4,5,5},{4,5,6},{4,6,6},{5,5,5},{5,5,6},{5,6,6} ,{6,6,6}]

A sequence 2009-09-19
From Oliver:
I am struggling to work out the missing terms in the following sequence:

1, 3, _, 7, 11, 18, _

Successive differences 2009-06-18
From Jonathan:
I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help.
Answered by Robert Dawson and Penny Nom.
Jon's bank account 2009-01-03
From Abigail:
Hi, i have an exam soon (monday =[ ) in my revison book, it shows two peoples bank accounts- and then it says

"write a formula to show the balence of Jon's bank account after n weeks of 2003" this is the table show

Jon's Bank account

 Weeks Balance(£) Week 1 Week 2 Week 3 Week 4 Week 5 970 1035 1100 1165 1230

0.151515...=15/99 2008-09-08
From Emma:
This week, my Algebra teacher told us about the pattern between infinitely repeating decimals and their corresponding fractions. (ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.) I was just wondering the reason why this pattern occurs. Is there a certain element that causes this pattern to occur?
Thanks
-Emma

Practical applications of sequences 2008-01-01
From carl:
can you give me examples of different kinds of practical applications of sequences?
Two sequences 2007-11-14
From Kim:
Pattern........what comes next?

1,4,9,16,25,_____,____
1,4,9,16,27,40,__________,_______

Answered by Penny Nom and Gabe Potter.
The nth term 2006-12-14
From Hepzibah:
what is the definition of nth term and n?
How many sequences are possible? 2006-10-28
From Sam:
A fair eight-faced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible?
Arithmetic progressions 2006-01-31
From A student:
1)the sum to n terms of a particular series is given by Sn=17n-3n2

a)find an expression for the n term of the series
b)show that the series is an arithmetic progression

2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference

A sequence of circles and tangents 2006-01-16
From Paul:
Consider a circle whose center is (2,2) and whose radius is 1, and the straight line that goes through the origin and that is tangent to this circle so that the intersection between them is as shown in the attached picture. With this new point we make a new circle whose radius is half of the first one, and we calculate the corresponding intersection point with the same suppositions as in the first case. We repeat the process to the infinite. Find the distance between the center of the circle in the infinite and the origin (point (0,0)).
Find the next 5 terms 2005-09-24
From Grant:
n+7, 2n-0.5, 4n. Find the next 5 terms of each one and explain the sequence in words
Find the first five terms of this sequence? 2005-09-17
my homework says can you find the first five terms of this sequence? 5n-6 i can`t figure it out.
Finding the nth term 2005-09-12
From Paul:

Hi , Im having a problem helping my daughter to find the Nth Term in the following sequences.

1/3 1/2 3/5 2/3

and

1 3 6 10

Geometric sequences 2004-02-03
From Alan:
hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative.
The 4th difference 2003-11-17
From Jack:
If i had a sequence which was the same at the 4th difference, aka difference to the 4th, like:

1 5 14 30 56 96 (sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1

then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an4+bn3+cn2+dn+e

Two sequences that agree in the first 4 terms 2003-05-26
From A student:
Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest?
Finite differences 2003-02-10
From Jenny:

I need to find a formula that will work with any number.
I am finding the volume of a 3d cross- shape. Here are my results so far:

```Term Number      0   1    2    3     4      5
nth term         1    7   25   63   129    231
1rst diff           6   18   38   66     102
2nd diff              12    20   28   36
3rd diff                  8     8    8
```

I can't seem to find a formula that will work with any number. Any help would be much appreciated.

Sums of evens 2002-09-14
From Rosa:
How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + ....
Answered by Leeanne Boehm and Harley Weston.
What is the next term? 2002-06-21
From A student:
What is the next term in the sequence:

1, 5, 14, 30.....

Sequences that agree on their first four terms 2002-05-16
From Mike:
Are there two formulas that define sequences that agree on their first four terms, but differ on the fifth term and all succeeding terms?
1,4,27,____,_____46656 2002-02-21
From Brenda:
1,4,27,____,_____46656..... please find the fourth and fifth numbers in this sequence.
Number sequences 2001-11-17
From Stephanie:
My name is Stephanie. My grade 7 math class is studying number sequences and, to me, they make almost no sense at all. Here I wrote down 2 of the many problems I have for homework and was wondering if you could explain them to me (I have to find the next 3 numbers in each sequence.) It would be a big help!

10, 14, 18, 22, _, _, _.

12, 21, 39, 75, _, _, _.

Find the pattern 2001-09-26
From A parent:
MY SON HAD ON A WORKSHEET WHAT I HAVE LISTED BELOW, BUT WE CAN'T SEEM TO FIND THE PATTERN. MOST THE TIME WE CAN, BUT THIS ONE IS DIFFERENT.

6,___, 9,____,____,_____,_____,_____

Four sequences 2001-09-24
From Nicole:
I have a few questions I couldn't figure it out. So any help will be great to find the next three numbers or letters. Here's the patters...
1. DEGHNORY, EHILMU, HIILMTU, BEILLMRUY,...

2. 50, 33, 25, 20, 16, 14, 12,...

3. 1777, 1795, 1818, 1819, 1820, 1822, 1836, 1837..

4. A,H,I,M,O,T,...

Answered by Chris Fisher and Penny Nom.
Arithmetic sequences 2001-09-10
From Rachel:
I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n-1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting -9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given.
Geometric and arithmetic sequences 2001-01-26
From Garry:
what are the equations for geometric and arithmetic sequences?

also, what are the equations for finding the sums of those series?

Answered by Leeanne Boehm and Penny Nom.
Some terms in a sequence 2001-01-15
From jamie:
Please help as soon as possible! i am stuck with some terms in a sequence. the terms are 1st term=1, 2nd term=10, 3rd term=35, 4th term=84, 5th term=165, 6th term=286. can anyone tell me the formula for the nth term? n is term number
The sum of the squares of 13 consecutive positive integers 2000-08-25
From Wallace:
Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square.
Covering 1, 1/2, 1/3,... 2000-08-22
From Wallace:
Consider the points 1, 1/2, 1/3, ... on the real number line. You are given five small bars, all of length p, which are to be placed on the number line such that all points will be covered. What is the minimum value of p that will allow you to do this?
Patterning and Sequencing 2000-07-05
From Michael Jellis:
What would be the next two terms?

1.0,0.5,0.6,0.75,0.8,___,____

please explain!!! I am completely baffled and need all the help I can get!

A sequence 2000-06-16
From Claire Hall:
Can you find the formula for the pattern 4,12,24,40,60
Geometric sequences 2000-04-11
From Jodie:
I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much!
Number sequences 1999-11-11
From Justin Schessler:
I CAN NOT figure out this sequence or how we continue this sequence...

3,2,6,5,15,14,___,___,___
Answered by Chris Fisher and Harley Weston.

Where three sequences meet. 1999-03-06
From Ali:
My name is Ali and I am in the 5th grade.

I have a math question:

What is the least positive integer meeting each of the following conditions:

• Dividing by 7 gives a remainder of 4
• Dividing by 8 gives a remainder of 5
• Dividing by 9 gives a remainder of 6
Help!